Studying the course of Covid-19 by a recursive delay approach

TL;DR

This paper introduces the SEPAR$_d$ epidemic model incorporating asymptomatic and unrecorded cases, compares it with classical models, and applies it to COVID-19 data from multiple countries to analyze disease dynamics and intervention effects.

Contribution

The paper generalizes recursive epidemic modeling to include the dark sector and delay differential equations, providing a better fit for COVID-19 data and insights into intervention timing.

Findings

SEPAR$_d$ model fits COVID-19 data across countries effectively.

Shortening quarantine and hospitalization delay can significantly flatten infection curves.

Model comparison suggests SEPAR$_d$ outperforms classical SIR in capturing COVID-19 dynamics.

Abstract

In an earlier paper we proposed a recursive model for epidemics; in the present paper we generalize this model to include the asymptomatic or unrecorded symptomatic people, which we call {\em dark people} (dark sector). We call this the SEPAR$_d$-model. A delay differential equation version of the model is added; it allows a better comparison to other models. We carry this out by a comparison with the classical SIR model and indicate why we believe that the SEPAR$_d$ model may work better for Covid-19 than other approaches. In the second part of the paper we explain how to deal with the data provided by the JHU, in particular we explain how to derive central model parameters from the data. Other parameters, like the size of the dark sector, are less accessible and have to be estimated more roughly, at best by results of representative serological studies which are accessible, however, only for a few countries. We start our country studies with Switzerland where such data are available. Then we apply the model to a collection of other countries, three European ones (Germany, France, Sweden), the three most stricken countries from three other continents (USA, Brazil, India). Finally we show that even the aggregated world data can be well represented by our approach. At the end of the paper we discuss the use of the model. Perhaps the most striking application is that it allows a quantitative analysis of the influence of the time until people are sent to quarantine or hospital. This suggests that imposing means to shorten this time is a powerful tool to flatten the curves